
Thus, perfect graphs could be a plausible class of graphs which answers Problem , since a graph \(G\)  is called perfect if for any induced subgraph \(H\)  of \(G\) , \(\omega (H)=\chi (H)\) . For any graph \(G\) , \(\omega (G)\le \chi _{\text{f}}(G)\le \chi (G)\)  [1]}, and so if \(G\)  is perfect, then \(\chi _{\text{f}}(G)=\omega (G)\) . Complete graphs and bipartite graphs are perfect graphs, but are all perfect graphs a part of the solution of Problem ?
